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    Öğe
    Analysis of a TB and HIV co-infection model under Mittag-Leffler fractal-fractional derivative
    (Iop Publishing Ltd, 2022) Liu, Xuan; Ahmad, Shabir; Rahman, Mati Ur; Nadeem, Yasir; Akgul, Ali
    In this paper, the nonlocal operator with the Mittag-Leffler kernel is used to analyze a TB-HIV co-infection model with recurrent TB and exogenous reinfection. The non-negative invariant region and basic reproduction number of the proposed model are demonstrated. By using the Krasnoselskii fixed result, we investigate that the TB-HIV co-infection model possesses at least one solution. We look at the existence of a unique solution using Banach's fixed point theorem. Functional analysis is used to demonstrate Ulam-Hyres stability. The numerical solution of the given model is obtained using the Adams-Bashforth technique. We illustrate the achieved results by studying the co-infection of TB and HIV for different fractional and fractal orders.
  • [ X ]
    Öğe
    Fractional Order Mathematical Model of Serial Killing with Different Choices of Control Strategy
    (Mdpi, 2022) Rahman, Mati Ur; Ahmad, Shabir; Arfan, Muhammad; Akgul, Ali; Jarad, Fahd
    The current manuscript describes the dynamics of a fractional mathematical model of serial killing under the Mittag-Leffler kernel. Using the fixed point theory approach, we present a qualitative analysis of the problem and establish a result that ensures the existence of at least one solution. Ulam's stability of the given model is presented by using nonlinear concepts. The iterative fractional-order Adams-Bashforth approach is being used to find the approximate solution. The suggested method is numerically simulated at various fractional orders. The simulation is carried out for various control strategies. Over time, all of the compartments demonstrate convergence and stability. Different fractional orders have produced an excellent comparison outcome, with low fractional orders achieving stability sooner.